Solve 1/x^2+2x+1+4/x+2x^2+x^3=5/2x+2x^2

$$\frac { 1 } { x ^ { 2 } + 2 x + 1 } + \frac { 4 } { x + 2 x ^ { 2 } + x ^ { 3 } } = \frac { 5 } { 2 x + 2 x ^ { 2 } }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+1\right)^{2}, the least common multiple of x^{2}+2x+1,x+2x^{2}+x^{3},2x+2x^{2}.

$$2x+2\times 4=\left(x+1\right)\times 5$$

Multiply 2 and 4 to get 8.

$$2x+8=\left(x+1\right)\times 5$$

Use the distributive property to multiply x+1 by 5.

$$2x+8=5x+5$$

Subtract 5x from both sides.

$$2x+8-5x=5$$

Combine 2x and -5x to get -3x.

$$-3x+8=5$$

Subtract 8 from both sides.

$$-3x=5-8$$

Subtract 8 from 5 to get -3.

$$-3x=-3$$

Divide both sides by -3.

$$x=\frac{-3}{-3}$$

Divide -3 by -3 to get 1.

$$x=1$$